1. Combine the fish trimmings, chopped onions, bay leaf, 1 teaspoon of salt and the 6 cups of water in a heavy 3- to 4-quart enameled or stainless-steel casserole. Bring to a boil over high heat, reduce the heat to low, and simmer partially covered for 30 minutes.

2. Strain the entire contents of the casserole through a fine sieve into a deep bowl, pressing down hard on the fish trimmings and onions with the back of a spoon to extract all their juices before discarding them.

3. Pour the stock back into the casserole and add the chopped fish. Stirring occasionally, bring to a boil over high heat. Reduce the heat to its lowest point and simmer uncovered for about 15 minutes, or until the fish can be easily mashed with the back of a spoon.

4. Puree the contents of the casserole in a food mill, or rub them through a coarse sieve, and return to the casserole. Stir in the 1 teaspoon of salt and ¼ teaspoon of pepper, and immerse the fish steaks in the soup.

5. Bring to a simmer over moderate heat and poach partially covered for 5 to 8 minutes, or until the fish flakes easily when prodded gently with a fork. Do not overcook.

6. With a slotted spatula, transfer the steaks to a large heated tureen or individual soup plates. With a whisk, beat 1 cup of the soup into the garlic paste and pour the mixture into a sauceboat.

7. Add the cucumber and vinegar to the remaining soup, taste for seasoning, and ladle over the fish steaks. Serve at once, accompanied by the garlic sauce.